1. Field of the Invention
The invention is related generally to the field of interpretation of measurements made by well logging instruments for the purpose of determining the properties of earth formations. More specifically, the invention is related to a method for determination of formation resistivity using array resistivity data in vertical and deviated wells.
2. Background of the Art
Electromagnetic induction, wave propagation, and galvanic logging tools are commonly used for determination of electrical properties of formations surrounding a borehole. These logging tools give measurements of apparent resistivity (or conductivity) of the formation that when properly interpreted are diagnostic of the petrophysical properties of the formation and the fluids therein.
The physical principles of electromagnetic induction resistivity well logging are described, for example, in, H. G. Doll, Introduction to Induction Logging and Application to Logging of Wells Drilled with Oil Based Mud, Journal of Petroleum Technology, vol. 1, p. 148, Society of Petroleum Engineers, Richardson Tex. (1949). Many improvements and modifications to electromagnetic induction resistivity instruments have been devised since publication of the Doll reference, supra. Examples of such modifications and improvements can be found, for example, in U.S. Pat. Nos. 4,837,517; 5,157,605 issued to Chandler et al, and U.S. Pat. No. 5,452,761 issued to Beard et al. Other tools include the HDLL (High Definition Lateral Log) of Baker Hughes Incorporated, described in U.S. Pat. No. 6,060,885 to Tabarovsky et al., and any generic Array Laterolog tools, e.g., the High-Resolution Laterolog Array tool (HRLA) of Schlumberger Inc.
Analysis of measurements made by any array induction logging tool, for example such as that disclosed by Beard and galvanic logging tools such as the HDLL and HRLA or any generic Array Laterolog tools, is based on inversion.
One problem with inversion is that the earth is characterized by a 2-D model (layers with radial changes in resistivity within each layer) or a 3-D model (layers with radial changes in resistivity within each layer, and a relative dip between layers and the borehole). A rigorous 2-D or 3-D inversion techniques would be quite time consuming and impractical for wellsite implementation. See, for example, Mezzatesta et al., and Barber et al. Several methods have been used in the past for speeding up the inversion. Frenkel et al. (SEG Extended Abstracts, 1995; SPE #36505, 1996) and in U.S. Pat. No. 5,889,729 to Frenkel et al., having the same assignee as the present invention and the contents of which are fully incorporated herein by reference disclose a so-called rapid well-site inversion method suitable for well-site (not a real-time) processing of array resistivity data. A rapid inversion method allows for substantially reducing the computational time by subdividing the 2-D/3-D problem into a sequence of smaller 1-D problems. Griffiths et al. (SPWLA 1999, paper DDD) disclose a so-called 1-D+1-D method of well-site (not a real-time) processing of HRLA logs. The processing consists of the following steps: borehole correction, 1-D inversion of individual logs in z direction (shoulder-bed-correction), and 1-D radial inversion of the corrected logs. The main shortcomings of this method are it does not satisfy a real-time processing requirements and it may provide inaccurate results in thin invaded layers due to coupling between shoulder beds and invasion in the adjacent layers. So it leads to significant errors in thin invaded layers. To check the quality and correct inversion results, Griffiths et al. suggest to run a rigorous 2-D inversion which makes this technique is not applicable to even post-acquisition well-site processing.
Prior art methods for real-time well-site interpretation typically perform the 1-D radial inversion on a point by point basis. Shoulder bed effects and borehole deviation effects are not considered. Correction is made only for the invasion effect and could be approximate and lead to incorrect 1-D inversion results even in relatively thick (˜5 ft or 1.5 m) invaded formations. In addition, the inversion process may become unstable at layer boundaries, so that significant post inversion processing is often required. This filtering results in a curve of Rt (true formation or virgin zone resistivity) that frequently looks little different from the deep-reading logs of focused curves and produces little additional information. There is a need for a method of real-time well-site inversion of array resistivity measurements that does not suffer from these drawbacks. The present invention addresses this need.